39257 ÷ 2 = 19628 R1
Alright, let's work through the division of 39257 by 2 step by step.

Step 1:
2 goes into 3 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 2 from 3 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 2

Step 2:
2 goes into 19 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 19
Subtract 18 from 19 to get 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 2

Step 3:
2 goes into 12 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 196
Subtract 12 from 12 to get 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 2

Step 4:
2 goes into 5 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 1962
Subtract 4 from 5 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 2

Step 5:
2 goes into 17 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 19628
Subtract 16 from 17 to get 1.

The final result is 19628 with a remainder of 1.